Hi ShelterLeopard.
I hiked the LT in (mostly) September of '06, finishing in the north on the 21st. I never saw full autumn colours on that trip and I suspect the peak that year (in the north) was probably a week or two after I finished. I don't know how typical that year was though as I am not a Vermonter and it was a wetter than average September. I think I saw the first hints of colour sometime around the 12th(?) of September, with significant patches of pretty pre-peak leaves in the last week of my hike. Many hikers have September and October LT pictures up on trailjournals from several years if you want a really good idea; but be wary of upload date vs. actual date.
Temperatures in September were nice and cool, with only a couple of below freezing nights and only a couple of hot days. There was no significant snow; only a couple of days with flurries.
Socially, there were quite a few hikers of all types on most days, though I did spend a few nights alone (mostly in the north).